Optimal trajectory planning of free-floating space robot using indirect approach in point to point motion

In this paper, a new method on the base of the indirect solution of optimal control problem is presented for trajectory planning of Free-Floating Space Robot (FFSR) in point to point motion. To this end, dynamic equations of the system beside the non-holonomic constraints due to angular momentum conservation low are derived in the state space form. Then the necessary conditions for optimality are derived using the fundamental theorem calculus of variations. The obtained equations lead to a two-point boundary value problem (BVP) which its solution result in optimal trajectory and optimal control function. In the proposed method, both manipulator and base moves from the initial pose to the final pose in such a way that all the boundary conditions, dynamic equations and non-holonomic constraints are satisfied, and a given performance index such as consumed power or torque is also minimized. Simulations are performed for a two-link free-floating space manipulator and the obtained results are compared with the previous works, and the efficiency of proposed method to reduce the base movement is illustrated.